Biomedical Engineering Reference
multiplied to R T E . However, computation of this rotation matrix can be integrated
easily into the above described system of linear equations.
5.1.2 Gravity Compensation and Tool Calibration
With the FT sensor calibrated to the robot's end effector, we are now able to detect
impacts (measured as forces and torques) on the mounted tool in robot coordinates.
However, due to gravity, the tool's weight affects the sensor and consequently the
To measure and detect these impacts with the sensor, e.g., user interaction or a
collision, we have to compensate for the tool's weight. By changing spatial ori-
entation of tool and sensor, the influence of the weight on the recordings changes.
Hence, we need to consider the gravity force depending on the current robot end
effector orientation R T E . Therefore, we have to apply the transform E T FT from the
robot's end effector to the sensor, accordingly.
Any tool mounted to the FT sensor has its specific tool parameters. Its gravity
force f g depends on the tool's mass (weight) m and the gravity acceleration
g ¼ 9 : 81 m/s 2 . The gravity force can be calculated as:
f g ¼ m g :
ð 5 : 9 Þ
Furthermore, the tool consists of a specific centroid s which is the center of
gravity. At s the gravity force acts and results in torques M G , as presented in
Eq. ( 5.1 ). However, s is not purely tool specific. As s is represented in the FT
sensor's coordinate frame, i.e. with respect to the origin of the FT sensor, the way
the tool is mounted is important, too. Thus, s changes with re-mounting, whereas f g
For any tool (re-)mounted to the FT sensor we must therefore estimate f g and s.
With a known end effector orientation, we are then able to subtract the gravity part
on the force and torque measurements for that orientation. In this way, we can use
the gravity compensated forces and torques to record impacts on the tool.
To calculate the tool parameters, again we use a set of n initial measurements
(F i ; M i ).
Eq. ( 5.6 )
throughout the recordings:
f g ¼ 1
ð 5 : 10 Þ
i ¼ 1
Subsequently, we use Eq. ( 5.1 ) with the recorded measurements to compute the
M i ¼ F i s ;
8 i 2½ 1 ; n ;
ð 5 : 11 Þ